Fractional calculus has made great strides in many fields of mathematics and science over the past several years. On the one hand, more modern definitions of fractional derivatives and integrals have extended the traditional definitions in some way. Furthermore, a current field of study in mathematical analysis is the thorough consideration of the functional features of these new concepts. Systems involving differential equations with fractional-order operators have undergone thorough analytical and numerical investigation, and prospective applications in the sciences and in technology have been suggested. This Special Issue’s goal is to provide a specialized venue for the discussion of new developments in the theory of fractional calculus and their applications. We encourage authors to submit excellent reports on a variety of fascinating research topics, including the analysis of fractional-order differential/integral equations, the evaluation of novel definitions of fractional derivatives, numerical approaches to fractional-order equations, and applications to physical systems governed by fractional differential equations.